Risks from spreading earthquake losses through the economy

general approach

We set out to create a stochastic earthquake catalog that is coherent with the seismic hazard model for the area under study. We then simulate the occurrence of the first earthquake in the catalog and calculate the physical damage (direct losses) from buildings, factories and infrastructure using traditional probabilistic seismic hazard assessment techniques. Direct losses perturb the initial equilibrium of the CGE model, so we restart it until it reaches a new equilibrium, but with different levels of output and prices, allowing to calculate the losses from this specific event. The analysis is then repeated for each event belonging to the stochastic earthquake catalog. Finally, we calculate various probabilistic hazard measures, including the effects of indirect losses, using the results obtained for all earthquakes. The remainder of this section will explain our approach and each of its components in some depth.

Earthquake Hazard Model

First, the seismic hazard model contains the exposure database 51,52,53,54,55 that includes all assets at risk relevant to the analysis. In our case, the relevant assets are buildings, factories, infrastructure, and, in general, all assets that provide inputs of some kind into the economic model. In other words, all assets whose damages may have a potential impact on economic flows. Each asset must be identified by its location, characteristics of seismic vulnerability, and the economic sector to which it belongs, particularly in relation to our present purposes.

At random moments, with all the origins remaining intact and after the Poisson process, the economic equilibrium is disturbed by an earthquake with known focal characteristics (magnitude, central position, orientation of the rupture plane), which in turn will produce a spatially random intensity field (peak Earth acceleration, spectral values). In contemporary seismic hazard models, this information is provided by the hazard component 56,57,58,59. This component provides a potentially very large set of events, each associated with an annual event frequency and one or more intensity random fields. Therefore, the hazard component provides information about how frequently different types of earthquakes occur and gives probabilistic indicators of the intensity that it produces. In principle, the hazard component should contain information about the frequencies of occurrence and the intensity distributions of all earthquakes that could occur in the future. In other words, the set of events must be collectively comprehensive.

Once a hypothetical earthquake has occurred, and its intensity – or more precisely, the intensity probability distributions – are known – the 60 Seismic Hazard Model provides tools for assessing the level of direct losses incurred by each of the assets in the exposure database; This part of the model is usually referred to as the loss component. The level of damage to the asset depends on its location, severity and vulnerability characteristics. Thus, once a hypothetical event occurs, we have means to determine the probability distribution of losses incurred by each of the assets at risk using special functions called vulnerability functions 60,61,62 that we used to characterize the seismic vulnerability of non-residential buildings belonging to economic sectors in Chile. Supplementary Note 2 in the Supplementary Material describes the characteristics and specifications of the probabilistic seismic hazard model used in this work for Chile.

In general, given the lower geographic resolution of CGE models compared to seismic hazard models, loss aggregation is required in order to sum all losses that correspond to the same economic sector in the same economic region. Since losses in different assets are not fixed numerical values ​​but are correlated random variables, the aggregation process is not trivial because of the correlation between losses for the same event. Supplementary Note 3 presents the loss aggregation process used in our study.

Therefore, as can be seen, a seismic hazard model is used in our approach to determine two basic pieces of information for each individual member of the event set: (i) the probability distributions of losses incurred by assets belonging to all economic sectors and regions, i.e., the intensity of direct losses; and (ii) the annual frequency with which the specified loss scenario occurs. We will see later how this information is used in the calculations of aggregate risk.

To date, the use of the seismic hazard model is not at all different from its classical use in risk assessment. However, we will see later how the results of these classic risk model are used as inputs in economic modelling.

economic model

We use BMCH, the Chilean version of the B-MARIA (Brazilian Multisectoral, Regional and Interregional Analysis Model), a fully functional CGE spatial model for Chile. The model uses an approach similar to 63,64,65 for integrating the interregional economic structure. We use an absorption matrix as a basis for calibrating the CGE model, along with a set of elasticities borrowed from the standard economic literature applied in Chile. This database allows economy-wide impacts to be captured through a complex scheme of input-output relationships.

The current version of the BMCH model recognizes the economic structures of the 15 Chilean regions. The results are based on a bottom-up approach – that is, national results are obtained from the compilation of regional results. The model identifies 12 production/investment sectors in each region that produce 12 commodities, a representative household in each region, regional and central governments, and one foreign region that trades with each local region. Two main local factors are used in the production process, according to regional endowments (capital and labour). It defines specific sets of government fiscal equations, cumulative relationships, and regional labor markets. The BMCH model qualifies as a Johansen-type model where the solutions are obtained by solving the model’s system of linear equations, in accordance with the Australian tradition. The typical result shows the percentage change in the set of endogenous variables after the policy is implemented, compared to its values ​​in the absence of such a policy, in a given environment. Regional links play an important role in the workings of the model. These links are driven by trade relations (goods flows) and the movement of factors (capital and labor migration). interregional trade flows are integrated; The relationships between inputs and outputs are required to calibrate the model, and inter-regional trade flexibility plays an important role. Supplementary Note 4 in the Supplementary Material provides the full specification of the model.

When an earthquake occurs, it produces direct losses, the probability distributions of which were determined using the earthquake hazard model described briefly in the previous subsection. Once aggregated, direct losses by sector and region are entered into the CGE model as “shocks” for the capital stock component of the sector/region group. These shocks are nothing more than external reductions in the capital stock, and are usually computed as the ratio between the physical loss and the total cost of the capital stock. When entering into the set of shocks in the CGE model, the equilibrium conditions for the model are lost, so we need to restart the CGE model to reach a new equilibrium that reflects how the economy has adapted to the shock received. The new state of equilibrium is obtained by a new set of values ​​of the endogenous variables, which are the results of the model.

A CGE model can be made from hundreds or even thousands of variants (external and internal); Each can provide us with a different type of outcome, whether of economic or social benefit. The richness of the CGE model in terms of the number of results is extraordinary, which allows the possibility of developing a wide range of analyzes. At the outset, we will focus on the variables that determine the total output of industries; However, later we will analyze other types of non-economic losses.

We will define the production loss for sector i in the j spatial region, Lpij, as the difference between production before and after the earthquake for the same sector/area. In other words, as a result of the fall in the stock of capital in specific sectors and regions hit by the earthquake, the economy achieves a new equilibrium in which production in that sector/area is smaller (or higher) after the earthquake than before. We consider this difference as a production loss, and this will be our initial measure of indirect losses, although we’ll explore using the results for other variables later.

At this initial stage of our research, the behavioral parameters and structural coefficients of the CGE model, the parameters and coefficients required to establish the relationships between exogenous and endogenous economic variables, are deterministic. Despite this, the outputs of the CGE model – indirect losses – are not constant numeric values, but rather random variables, because some of the inputs were also random variables. The probability distributions of all relevant CGE model outputs, either at the sector/area level or for any desired aggregation, are obtained during modeling.

At this point, we can calculate the probabilistic direct and indirect losses for each event from the set of events. The next section will explain how the most popular risk measures can be obtained from the results presented to date.

Risk Measures

The most common risk metrics, both in the world of disaster risk management and in the insurance sector, are: (i) average annual loss; and (ii) the loss-exceeding curve, which indicates the average frequency with which certain values ​​of loss will be exceeded. We will focus only for illustrative purposes on total direct and indirect losses. Total losses, of course, are the sum of losses for all assets, in the case of direct losses, and for all sectors and regions, in the case of indirect losses.

For example, event k for the event set results in direct and indirect probability losses Ldk and Lpk, respectively. Then, the corresponding average annual losses, AALd, and AALp will be given by:

$${AA}{L}_{d}=\mathop{\sum}\limits_{k=1}^{{Events}}{{{{\rm{E}}}}}({{ Ld }}_{k}){F}_{k}$$

(1)

$${AA}{L}_{p}=\mathop{\sum}\limits_{k=1}^{{Events}}{{{{\rm{E}}}}}({{Lp }}_{k}){F}_{k}$$

(2)

where E (.) is the expected value and Fk is the annual frequency of occurrence of event k. AALd is a quantity that is routinely calculated in traditional risk analyses; AALp is presented in this paper.

The loss overrun curves, d (.) and p (.) for direct and indirect loss, respectively, are calculated with the following expressions:

$${\nu }_{d}(l)={\mathop{\sum}\limits_{k=1}^{{Events}}}{\Pr}({Ld}_{k}\,> \, l) {F}_{k}$$

(3)

$${\nu }_{p}(l)={\mathop{\sum}\limits_{k=1}^{{Events}}}{\Pr}({Lp}_{k}\,> \, l) {F}_{k}$$

(4)

where Pr (Ldk > l) and Pr (Lpk > l) are, respectively, the probability of direct and indirect losses exceeding a certain value, l. In this case, νp (.) is presented in this paper.

Complementary Risk Indicators

The procedure for calculating the measures of probabilistic risk with respect to employment, GRP, CPI, volume of exports and any other economic variable of the CGE model is the same but for the corresponding economic variable rather than the production variable (indirect loss). In the case of positive economic effects, the calculation procedure is again the same, with the difference that, in this case, we only consider the positive effects caused by each earthquake in the CGE model.

The risk calculations described in this paper were performed using the DIRAS-2020 software, developed at the Instituto de Ingeniería, UNAM. This software was specifically created to join and process information from the traditional seismic hazard model and the spatial CGE model.

Report summary

More information about research design is available in the Nature Research report summary associated with this article.

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